Pontryagin's Principle of Mixed Control-State Constrained Optimal Control Governed by Fluid Dynamic Systems

Abstract

This article deals with Pontryagin's minimum principle for optimal control problems governed by an abstract fluid dynamical system with mixed control-state constraints. Two techniques are mainly used to obtain our results: ϵ-perturbation for admissible control set and diffuse perturbation for admissible control. Using these results, the necessary conditions for L 2-local optimal solution of our control problems can be studied under some assumptions. In the end of this article, these results are applied to some special fluid dynamical systems which contain the fluid systems driven by its boundary and magnetohydrodynamics(MHD).